The motion and annihilation of a grain boundary (GB) in graphene are investigated by tight-binding molecular dynamics (TBMD) simulation and ab initio local density approximation total energy calculation. A meandering structure of the GB is found to be energetically more favorable than other structures, in good agreement with experiment. It is observed in the TBMD simulation that evaporation of carbon dimers and sequential Stone-Wales transformations of carbon bonds lead to rapid motion and annihilation of the GB. The dimer erection and evaporation are found to proceed by formation of an adatom due to bond breaking. These results shed interesting light on the fabrication of high-quality graphene.